Men's interest in/for developing

Men’s interest in/for developing a cure for cancer have promoted the rapid in the field of genetic.
Which one is correct and why not the other?

Your sentence is not quite right.
I suggest:
Man’s interest in developing a cure for cancer has promoted the field of genetics rapidly.

(Here ‘man’ is used as a general term for ‘mankind’)

I will ask you why not “for” here?